Calculation of areas – Definite Integral

 

Definite Integral of a function is used to calculate the areas of flat regions, which are delimited by curves and straight lines.

 

Areas of flat regions:

 

 

 

Bioprofe | Calculation of areas – Definite Integral | 04

Bioprofe | Calculation of areas – Definite Integral | 05

 

 

Areas limited by several functions:

 

 

This area is calculated as follows:

 

 
 

Functions whose graphs are waveform:

 

 

Examples:

 

Area delimited by the parabola y=x² and the line y=1

 

 

Integration interval:

 

Therefore:

 
 

Area delimited by the parabola y=x², the line y=-x+2 and the ox axis

 

 

 

Points of intersection:

 

It is applied the following formula:

 

Integration interval:
x=1
x=-2

 

Therefore:

 

 

Area delimited by the parabola y=-x², the lines x=-1, x=2 and the ox axis

 

 

 

Area delimited by the function y=x³, the lines x=-1, x=2 and the ox axis

 

 

It is solved:

 
 

Area delimited by the functions y=e^x, y=e^-x , the lines x=-1, x=1 and the ox axis

 

 

 

 

 

 

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